Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas

Abstract

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of “electric” or “magnetic” type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an “antiparticle.” Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (κ, ω₀, σ,l, m), where ω₀ is the mean of the angular frequencies of the plane waves making up the configuration, σ is the variance of those frequencies, κ is a positive constant with dimensions of action, andl, m are angular momentum “quantum numbers” withl a positive integer andm an integer such that ‖m‖≤l. The rest energy of the “particle” is κω₀, its spin is κ ‖m‖, and its lifetime is of the order of 1/σ. Its antiparticle has ω₀ replaced by −ω₀.